Is Quantum Mechanics a proper subset of Classical Mechanics?

TL;DR

This paper proposes that quantum mechanics is a projection of a deeper classical variational structure, with undecidability and computability limits explaining quantum phenomena and the classical-quantum boundary.

Contribution

It introduces a classical variational framework underlying quantum mechanics, explaining quantum phenomena through classical action and computability limits, challenging the traditional view of quantum theory as complete.

Findings

Classical action dynamics are generally undecidable.

Spectral gap undecidability parallels quantum spectral issues.

Experimental test proposed using double quantum dots.

Abstract

Quantum mechanics is widely regarded as a complete theory, yet we argue it is a tractable projection of a deeper, computationally-inaccessible classical variational structure. By analyzing the coupled partial differential equations of the Hamilton type 1 principal function, we show that classical action-based dynamics are generally undecidable, paralleling spectral gap undecidability in quantum systems. In near Kolmogorov-Arnold-Moser systems, stability hinges on Diophantine conditions that are themselves undecidable, limiting predictability via arithmetic logic rather than randomness. Phenomena like spin 3/2 systems and larger, quantum scars and Leggett inequality violations support this view, naturally explained by time symmetric classical action. This framework offers a principled resolution to the long standing dichotomy between unitarity and entanglement by deriving both as emergent features of a tractable rendering from a fundamentally non-separable classical variational geometry. Collapse and decoherence arise from representational limits, not ontological indeterminism. We propose an explicit experimental test using lateral double quantum dots to detect predicted deviations from standard quantum coherence at the classical chaos threshold. This reframing suggests the classical quantum boundary is set by computability and not by the Planck constant. Implications for quantum computing and quantum encryption are discussed.